Demodulation method using soft decision for quadrature amplitude modulation and apparatus thereof

ABSTRACT

The present invention relates to a demodulation method using soft decision for QAM (Quadrature Amplitude Modulation). In a soft decision method for demodulation of a received signal of square QAM comprised of the same phase signal component and a orthogonal phase signal component, the demodulation method using soft decision has a characteristic wherein the processing speed is improved, and the manufacturing expense is reduced by gaining a condition probability vector value, which is each soft decision value, corresponding to a beat position of hard decision using a function which includes a condition judgement operation from a orthogonal phase component value of a received signal and the same phase component value.

TECHNICAL FIELD

The present invention relates to a soft decision demodulation of anQuadrature Amplitude Modulation (hereinafter, referred to as QAM)signal, and more particularly, to a soft decision demodulation methodcapable of enhancing a process speed of soft decision usingpredetermined function and pattern upon demodulating a received signal.

BACKGROUND ART

QAM scheme is capable of transmitting loading two or more bits to agiven waveform symbol, whose waveform can be mathematically expressed intwo real numbers and imaginary numbers that do not interfere each other.That is, in a complex number imaginary number α+β i, a change of value αdoes not affect a value β. Due to that reason, an quadrature signalcomponent can correspond to α, and in-phase signal component cancorrespond to β. Generally, the quadrature signal component is referredto as Q-channel, and the in-phase component signal is referred to asI-channel.

A constellation diagram of QAM is to connect amplitudes of such twowaves with each other so as to make a number of combinations, positionthe combinations on a complex number plane to have an equal conditionalprobability, and promise such a position. FIG. 2 is a diagram showing anexample of such constellation diagram, whose size is 16 combinations.Also, each of points shown in FIG. 2 is referred to as a constellationpoint. Also, combinations of binary numbers written under eachconstellation diagram is symbols set to each point, that is, a bundle ofbits.

Generally, a QAM demodulator serves to convert signals incoming to an Ichannel and Q channel, that is, a received signal given as a α+β i intothe original bit bundle according to the promised position mentionedabove, that is, the combination constellation diagram. At this time,however, the received signals are not positioned on places assignedpreviously in most cases due to the effect of noise interference, andaccordingly he demodulator has to restore the signals converted due tothe noise to the original signals. However, since there is often someexcessivenesses to guarantee a reliability of communication in that thedemodulator takes a charge of the role of noise cancellation, it ispossible to embody more effective and reliable communication system byrendering the role to the next step of a channel decoder. However, sincethere is an information loss in a bit quantization process performed bya binary bit detector as in a hard decision by making a demodulationsignal having a continuous value to correspond to discrete signals of 2levels in order to perform such a process, a similarity measure withrespect to a distance between a received signal and the promisedconstellation point is changed from a Hamming distance to an Euclideandistance without using the binary bit detector, so that an additionalgain can be obtained.

As shown in FIG. 1, in order to modulate and transmit a signal encodedby a channel encoder and demodulate the signal in a channel demodulatorthrough a hard decision coding process, the demodulator has to have ascheme for generating the hard decision values corresponding to each ofthe output bits of a channel encoder from a receiving signal consistedof an in-phase signal component and a quadrature phase signal component.Such scheme generally includes two procedures, that is, a simple metricprocedure proposed by Nokia company and a dual minimum metric procedureproposed by Motorola, both procedures calculating LLR (Log LikelihoodRadio) with respect to each of the output bits and using it as an inputsoft decision value of the channel demodulator.

The simple metric procedure is an event algorithm that transforms acomplicated LLR calculation equation to a simple form of approximationequation, which has a degradation of performance due to an LLRdistortion caused by using the approximation equation even though itmakes the LLR calculation simple. On the other hand, the dual minimummetric procedure is an event algorithm that uses the LLR calculatedusing more precise approximation equation as an input of the channeldemodulator, which has a merit of considerably improving the degradationof performance caused in the case of using the simple metric procedure,but it has an expected problem that more calculations are neededcompared with the simple metric procedure and an its complication isconsiderably increased upon embodying hard ware.

DISCLOSURE OF THE INVENTION

Therefore, an object of the present invention is to solve the problemsinvolved in the prior art, and to provide a soft decision scheme fordemodulating a Quadrature Amplitude Modulation (QAM) receiving signalconsisted of an in-phase signal component and an quadrature phase signalcomponent, where a conditional probability vector value being each of asoft decision value corresponding to a bit position of a hard decisioncan be obtained using a function including a conditional determinationcalculation from an quadrature phase component value and an in-phasecomponent value of the received signal, and so it is expected thatprocess rate can be improved and a real manufacturing cost of hard warecan be reduced. In order to perform such a procedure, first, a knownform of a combinational constellation diagram of QAM and itscharacteristic demodulation scheme will be described as follows. Thecombinational constellation diagram of QAM may be generally divided into3 forms according to an arrangement of bit bundle set in theconstellation point. The First of it is a form constellated as shown inFIGS. 2 to 4, the second is a form constellated as shown in FIGS. 5 to7, and the third is a form not included in this application.

A characteristic of the form shown in FIG. 2 can be summarized asfollows. In the case that the magnitude of the QAM is 2^(2n), the numberof bits set in each point becomes 2n, where conditional probabilityvector values corresponding to the first half of the number, that is,the first to n^(th) bits are demodulated by one of the received signalsα and β and the conditional probability vector values corresponding tothe second half of the number, that is, the (n+1)^(th) to the 2n^(th)bits are demodulated by the remaining one receiving signal. Also, anequation that is applied to both demodulations has the same procedure inthe first half and second half demodulations. That is, when the value ofreceiving signal corresponding to the second half is substituted in thefirst half demodulation method, the result of the second half can beobtained. (Hereinafter, such form is referred to as ‘the first form’)

The characteristic of the form shown in FIG. 5 can be summarized asfollows. In the case that the magnitude of the QAM is 2n^(2n), thenumber of the bits set in each of the points becomes 2n, and thedemodulation method of the conditional probability vector correspondingto odd-ordered bit is the same as the calculation method of theconditional probability vector corresponding to the next even-orderedbit. However, the receiving signal value used to calculate theconditional probability vector corresponding to the odd-ordered bit usesone of α and β according to a given combination constellation diagramand the receiving signal value for the even-ordered bit is used for theremaining one. In other word, in the cases of the first and secondconditional probability vector calculations, they use the samedemodulation method but the values of the receiving signals aredifferent. (Hereinafter, such form is referred to as ‘the second form’).

BRIEF DESCRIPTION OF THE DRAWINGS

The above objects, other features and advantages of the presentinvention will become more apparent by describing the preferredembodiment thereof with reference to the accompanying drawings, inwhich:

FIG. 1 is a block diagram for explaining a general digital communicationsystem;

FIG. 2 is a view showing a combination constellation point forexplaining a soft decision demodulation method in accordance with afirst embodiment of the present invention;

FIGS. 3 and 4 are views for explaining a bit constellation in thecombination constellation diagram shown in FIG. 2;

FIG. 5 is a view showing a combination constellation diagram forexplaining a soft decision demodulation method in accordance with asecond embodiment of the present invention;

FIGS. 6 and 7 are views for explaining a bit constellation in thecombination constellation diagram shown in FIG. 5;

FIG. 8 is a view showing a conditional probability vector decisionprocedure in accordance with the present invention as a functionalblock;

FIG. 9 is an output diagram with respect to each conditional probabilityvector of a first form of 1024-QAM;

FIG. 10 is an output diagram with respect to each conditionalprobability vector of a second form of 1024-QAM;

FIG. 11 is a view showing a function applied to a first probabilityvector of a third embodiment of the present invention;

FIG. 12 is a view showing a function applied to a second probabilityvector of the third embodiment of the present invention;

FIG. 13 is a view showing a function applied to a first probabilityvector of the fourth embodiment of the present invention;

FIG. 14 is a view showing a function applied to a second probabilityvector of the fourth embodiment of the present invention; and

FIG. 15 is a view showing a hard ware configuration for a soft decisionof a first form of 64-QAM in accordance with the present invention.

BEST MODE FOR CARRYING OUT THE INVENTION

Reference will now be made in detail to a preferred embodiment of thepresent invention, examples of which are illustrated in the accompanyingdrawings.

The present invention remarkably improves process speed by applying aconditional probability vector equation instead of a log likelihoodratio method being a soft decision demodulation method of a square QAMsignal that is generally used in the industry.

A newly developed demodulation method of a square QAM signal is dividedinto 2 forms, and a first and a third embodiments are used for the firstform and a second and a fourth embodiments are used for the second form.Also, an output of the final conditional probability vector value coversan area between a real number “a” and another real number “−a”.

First, explaining several basic prerequisites before entering into thedescription, the magnitude of the QAM can be characterized by themathematical expression 1 and accordingly the number of bits set in eachpoint of the constellation diagram can be characterized by themathematical expression 2.2^(2n)−QAM. n=2, 3, 4   [mathematical expression 1]the number of bits set in each point=2n   [mathematical expression 2]

Accordingly, the number of the conditional probability vector valuesbeing the final output values also becomes 2n.

Now, a first one among the method for demodulating the square QAMsignals of the present invention will be explained.

First, a soft decision method of receiving signal of the square QAMsignal corresponding to the first form will be explained. In the case ofthe first form, although it was mentioned that one of values of thequadrature phase component (real number part or α) or the in-phasesignal component (imaginary number part or β) is used to calculate theconditional probability vector corresponding to the first half bitcombination when explaining the characteristic of the first form, thefirst half and the second half demodulate using the value β and value αrespectively, for the convenience of understanding and an output areaaccording to the demodulation is set as a value between 1 and −1 for theconvenience' sake in the following description. Also, k is used as aparameter indicating an order of each bit.

A method for calculating a conditional probability vector correspondingto the case that the first bit, that is, k is 1 in the first form can beexpressed as a mathematical expression 3, and FIG. 5 is a visualizationof it.

[Mathematical Expression 3]

In the case of the first conditional probability vector (k=1), outputvalue is determined as $\frac{1}{2^{n}}{\beta.}$However, the value of n is determined by the magnitude of QAM using themathematical expression 1.

A method for calculating the conditional probability vectorcorresponding to the second bit k=2) in the first form can be expressedby a mathematical expression 4, and FIG. 6 is a visualization of it.

[Mathematical Expression 4]

In the case of the second conditional probability vector C=2), theoutput value is unconditionally determined as$c - {\frac{c}{2^{n - 1}}{{\beta }.}}$

Here, n is a magnitude parameter of the QAM in the mathematicalexpression 1, and c is a constant.

A method for calculating a conditional probability vector correspondingto a third bit to n^(th) bit (k=3, 4 . . . , n−1, n) in the first formcan be expressed as a mathematical expression 5. Here, as can be seenfrom FIG. 9, since the conditional probability vector corresponding tothe third or later bit indicates a determined iteration (v shape) form,it is noted that an expression be repeatedly used using such property.

[Mathematical Expression 5]

First, dividing the output diagram with a basic v-shaped form, theconditional probability vector corresponding to each bit is divided into(2^(k−3)+1) areas.

{circle around (2)} A basic expression according to the basic form isdetermined as ${\frac{d}{2^{n - k + 1}}{\beta }} - {d.}$

{circle around (3)} If finding a belonging area as the given β andsubstituting a value of |β|−m that is subtracted a middle value m ofeach area (for example, since the repeated area is one when k=4, thearea becomes 2^(n−2)≦|β|<3·2^(n−2) and the middle value becomesm=2^(n−1)) into the basic expression as a new β, the output value can bedetermined.

{circle around (4)} Finally, in the left and right outer areas among thedivided areas, that is, (2^(k−2)−1)2^(n−k+2)<|β|, the output value canbe determined by substituting the middle value of m=2^(n) and (|β|−m)value of a new β into the basic expression.

Here, d is a constant that is changed according to a value of k.

A method for calculating the conditional probability vectorcorresponding to the second half bits of the first form, that is, bitnumber n+1 to 2n can be obtained by substituting the β into α in themethod for obtaining the conditional probability vector of the firsthalf according to the characteristic of the first form. In other word,the condition that all of β in the mathematical expression 3 aresubstituted with a becomes a calculation expression of the firstconditional probability vector of the second half, that is, aconditional probability vector corresponding to (n+1)^(th) bit. Theconditional probability vector corresponding to the (n+2)^(th) bit ofthe second conditional probability vector of the second half can bedetermined by substituting β with α in the mathematical expression 4that is the condition to calculate the second conditional probabilityvector of the first half, and the conditional probability vectorcorresponding to the bit number n+3 to 2n being the next case can bedetermined by transforming the mathematical expression to the abovedescription.

Next, a method for performing a soft decision of the receiving signal ofa square QAM corresponding to the second form will be explained. Forconvenience of understanding, demodulation is performed to determine theconditional probability vector corresponding to odd-ordered bits usingthe value of a and to determine the conditional probability vectorcorresponding to even-ordered bits using the value of β and accordinglythe output scope is determined between 1 and −1 as is in the first formfor convenience' sake.

In the second form, a method for calculating the conditional probabilityvector corresponding to the first bit (k=1) can be expressed as amathematical expression 6 and FIG. 6 is a visualization of it.

[Mathematical Expression 6]

{circle around (a)} In the case of the first bit (k=1), the output valueis determined as ${- \frac{1}{2^{2}}}{\alpha.}$

However, the value of n is determined by the mathematical expression 1according to the magnitude of the QAM.

In the second form, the conditional probability vector corresponding tothe second bit (k=2) can be obtained by substituting the α with β in themathematical expression 6 for calculating the first conditionalprobability vector according to the characteristic of the second form.

In the second form, a method for calculating the conditional probabilityvector corresponding to the third bit (k=3) can be expressed as amathematical expression 7.If α·β≧0.   [mathematical expression 7]

{circle around (a)} In the case of the third bit (k=3), the output valueis determined as ${\frac{c}{2^{n - 1}}{\alpha }} - {c.}$

If α·β<0, the calculation expression is determined as an expression inwhich all of α are substituted with β in the calculation expression inthe case of α·β≧0.

Here, n is a magnitude parameter of the QAM in the mathematicalexpression 1 and c is a constant.

As such, it can be another characteristic of the second form QAM thatthe conditional probability vector is obtained in the cases of α·β≦0 andα·β<0 separately. Such characteristic is applied when the conditionalprobability vector corresponding to the third or later bit of the secondform and includes a reciprocal substitution characteristic likesubstituting β with α.

An expression to obtain the conditional probability vector correspondingto the fourth bit (k=4) of the second form can be obtained bysubstituting α with β and β with α in the mathematical expression 7 usedto obtain the third conditional probability vector according to thesecond form.

The expression used to obtain the conditional probability vectorcorresponding to the fifth bit (k=5) of the second form can be obtainedby applying the mathematical expression 8. Here, as can be seen fromFIG. 10, since the conditional probability vector corresponding to thefifth or later bit indicates a determined an iteration (v shape) form,it is noted that an expression be repeatedly used using such property.However, when the conditional probability vector corresponding to thefifth or later bit is calculated, the even-ordered determination valueuses the expression that was used to calculate just before odd-ordereddetermination value according to the property of the second form, whichis applied when the magnitude of the QAM is less than 64 only. And, whenthe magnitude is over 256, the remaining part can be divided into twoparts and the calculation can be performed in the first half part andthen in the second half part as is in the first form.If α·β≧0   [mathematical expression 8]

{circle around (a)} First, on dividing the output diagram into a basicV-shaped form, the conditional probability vector corresponding to eachbit can be divided into (2^(k−5)+1) areas.

{circle around (b)} A basic expression according to a basic form isdetermined as ${\frac{d}{2^{n - k + 3}}{a}} - {d.}$

{circle around (c)} If finding a belonging area as the given α andsubstituting a value of |α|−m that is subtracted a middle value m ofeach area (for example, since the repeated area is one when k=6, thearea becomes 2^(n−2)≦|α|<3·2^(n−2) and the middle value becomesm=2^(n−1)) into the basic expression as a new α, the output value can bedetermined.

{circle around (d)} Finally, in the left and right outer areas among thedivided areas, that is, (2^(k−2)−1)2^(n−k+2)<|α|, the output value canbe determined by substituting the middle value of m=2^(n) and (|α|−m)value of a new β into the basic expression.

In the case of α·β<0, the output value can be obtained by substituting αwith β in the expressions (a), (b), (c) and (d).

The calculation of the conditional probability vector corresponding tothe sixth bit of the second form can be obtained by substituting α withβ and β with a in the mathematical expression 8 used to obtain the fifthconditional probability vector by the property of the second form in thecase that the magnitude of the QAM is 64-QAM. However, in the case thatthe magnitude of the QAM is more than 256-QAM, the first half isobtained by dividing total remaining vectors into 2 and the second halfis obtained by substituting the received value (α or β)) into theexpression of first half. At this time, changed value in the expressionof first half is the received value only, and the bit number value (k)is not changed but substituted with that of first half.

Consequently, in the case that the magnitude of the QAM is more than256, the calculation of the conditional probability vector correspondingto the fifth to (n+2)^(th) bit of the second half is determined by themathematical expression 8.

The calculation of the conditional probability vector corresponding tothe (n+3)th to the last, 2nth bit of the second form is determined bysubstituting the parameter α with β in the mathematical expression asmentioned above.

The soft decision demodulation of the square QAM can be performed usingthe received signal, that is, α+β i through the procedure describedabove. However, it is noted that although the method described abovearbitrarily determined an order in selecting the received signal andsubstituting it into a determination expression for convenience ofunderstanding, the method is applied in more general in real applicationso that the character α or β expressed in the mathematical expressionscan be freely exchanged each other according to the combinationconstellation form of the QAM and the scope of the output values may benonsymmetrical such as values between a and b, as well as values betweena and −a. It can be said that such fact enlarges the generality of thepresent invention, so that it increases its significance. Also, althoughthe mathematical expressions described above seems to be verycomplicated, they are generalized for general applications so that it isrealized that they are very simple viewing them through really appliedembodiments.

First Embodiment

The first embodiment of the present invention is a case corresponding tothe first form and is applied the property of the first form. The firstembodiment includes an example of 1024-QAM where the magnitude of QAM is1024. The order selection of the received signal is intended to apply αin the first half and β in the second half.

Basically, QAM in two embodiments of the present invention can bedetermined as following expression. A mathematical expression 1determines the magnitude of QAM and a mathematical expression 2 showsthe number of bits set in each point of a combination constellationdiagram according to the magnitude of QAM.2^(2n)-QAM, n=2, 3, 4   [mathematical expression 1]

[Mathematical Expression 2]

the number of bits set in each point =2n

Basically, the magnitude of QAM in the first embodiment of the presentinvention is determined as the following expression, and accordingly theconditional probability vector value of the final output value becomes2n.

A case where 2^(2*5)-QAM equals to 1024-QAM according to themathematical expression 1 and the number of bits set in eachconstellation point equals to 2×5=10 bits according to the mathematicalexpression 2 will be explained using such mathematical expressions 1 and2. First, prior to entering into calculation expression applications, itis noted that if a calculation expression for 5 bits of the first halfamong 10 bits are known by the property of the first form, a calculationexpression for remaining 5 bits of the second half is also knowndirectly.

First, the first conditional probability vector expression is a case ofk=1, and has its output value determined as $\frac{1}{2^{5}}\beta$unconditionally.

Next, the second (that is, k=2) conditional probability vector has itsoutput value of $c - {\frac{c}{2^{4}}{{\beta }.}}$Here, c is a constant.

Next, the third (k=3) conditional probability vector calculationexpression is given as follows, where the basic expression according tothe basic form is determined as ${\frac{d}{2^{3}}{\beta }} - {d.}$

At this time, the calculation is divided into 2 areas, and the outputvalue is determined as ${\frac{d}{2^{3}}{\beta }} - d$if |β|<2⁴, and output value is determined as${\frac{d}{2^{3}}{{{\beta } - 32}}} - d$for the other cases.

Next, the fourth (k=4) conditional probability vector calculationexpression is given as follows, where the basic expression according tothe basic form is determined as ${\frac{d}{2^{2}}{\beta }} - d$and divided into 3 areas.

Here, the output value is determined as${\frac{d}{2^{2}}{\beta }} - d$if |β|<2³, the output value is determined as${\frac{d}{2^{2}}{{{\beta } - 16}}} - d$if 2³≦|β|<3·2³, and the output value is determined as${\frac{d}{2^{2}}{{{\beta } - 32}}} - d$for the other case.

Next, the calculation expression of the fifth (k=5) conditionalprobability vector is given as follows, where a basic expressionaccording to the basic expression is determined as${\frac{d}{2}{\beta }} - d$and is divided into 5 areas. Here, the output value is determined as${{\frac{d}{2}{\beta }} - {d\quad{if}\quad{\beta }}} < {2^{2}.}$

And the output value is determined as${\frac{d}{2}{{{\beta } - 8}}} - d$if 2²≦|β|<3·2², the output is determined as${\frac{d}{2}{{{\beta } - 16}}} - d$if 3·2²≦|β|<5·2², the output value is determined as${\frac{d}{2}{{{\beta } - 24}}} - d$if 5·2²≦|β|<7·2², and the output value is determined as${\frac{d}{2}{{{\beta } - 32}}} - d$for other cases

Next, the calculation expression of 6^(th) to 10^(th) conditionalprobability vector is implemented by substituting α+β with α+β in thefirst to fifth conditional probability vectors according to the propertyof the first form.

Second Embodiment

The second embodiment of the present invention is a case correspondingto the second form and is applied the property of the second form. Thesecond embodiment includes an example of 1024-QAM where the magnitude ofQAM is 1024. The order selection of the received signal is intended toapply α first.

As is in the first embodiment, the mathematical expression 1 determinesthe magnitude of the QAM, and the mathematical expression 2 indicatesthe number of bits set in each point of the combination constellationdiagram according to the magnitude of the QAM.2^(2n)−QAM, n=2, 3, 4   [mathematical expression 1]the number of bits set in each point=2n   [mathematical expression 2]

Basically, the magnitude of QAM in the second embodiment of the presentinvention is determined as the above expression, and accordingly theconditional probability vector value of the final output value becomes2n.

A case where n equals to 5, that is, 2^(2*5)-QAM equals to 1024-QAMaccording to the mathematical expression 1 and the number of bits set ineach constellation point equals to 2×5=10 bits according to themathematical expression 2 will be explained when n is 5 using suchmathematical expressions 1 and 2.

First, the first conditional probability vector calculation is a case ofk=1, where the output value is determined as $\frac{1}{2^{5}}a$unconditionally.

Next, the second (k=2) conditional probability vector calculationexpression is a case where the first calculation expression issubstituted, where the output value is determined as$\frac{1}{2^{5}}{\beta.}$

Next, for the third (k=3) conditional probability vector calculationexpression, when αβ≧0, the following will be given, where the outputvalue is determined as $c - {\frac{c}{2^{4}}{a}}$unconditionally.

However, c is a constant.

When αβ<0, this calculation expression is obtained by substituting αwith β in the expression used for the method for determining the outputof the third conditional probability vector explained just above (αβ≧0).

Next, for the fourth (k=4) conditional probability vector calculation,

(1) when αβ≧0, the following will be given, where the output value isdetermined as $c - {\frac{c}{2^{4}}{\beta }}$unconditionally.

(2) When αβ<0, this calculation expression is obtained by substituting αwith β in the expression used for the method for determining the outputof the fourth conditional probability vector explained just above(αβ≧0).

Next, for the fifth (that is, k=5) conditional probability vectorcalculation expression,

when αβ≧0, the following will be given, where a basic expressionaccording to the basic form is determined as${\frac{d}{2^{3}}{a}} - {d.}$

Here, the expression is divided into 2 areas, where if |α|<2⁴, theoutput value is determined as ${{\frac{d}{2^{3}}{a}} - d},$and the output value is determined as${\frac{d}{2^{3}}{{{\alpha } - 32}}} - d$for other cases.

(2) When αβ<0, this calculation expression is obtained by substituting αwith β in the expression used for the method for determining the outputof the fifth conditional probability vector explained just above (αβ≧0).

Next, for the sixth conditional probability vector (that is, k=6),

when αβ≧0, a basic expression according to the basic form is determinedas ${{\frac{d}{2^{2}}{a}} - d},$and here, the expression is divided into 3 areas, where if |α|<2³, theoutput value is determined as ${{\frac{d}{2^{2}}{a}} - d},$the output value is determined as${{\frac{d}{2^{2}}{{{a} - 16}}} - d},$and the output value is determined as${\frac{d}{2^{2}}{{{\alpha } - 32}}} - d$for other cases.

When αβ<0, this calculation expression is obtained by substituting αwith β in the expression used for the method for determining the outputof the sixth conditional probability vector explained just above (αβ≧0).

Next, for the calculation expression of the seventh (k=7) conditionalprobability vector,

when αβ≧0, a basic expression according to the basic form is determinedas ${{\frac{d}{2}{a}} - d},$and here, the expression is divided into 5 areas,

where if |α|<2², the output value is determined as${{\frac{d}{2}{a}} - d},$

if 2²<|α|<3·2², the output value is determined as${{\frac{d}{2}{{{a} - 8}}} - d},$

if 3·2²<|α|<5·2², the output value is determined as${{\frac{d}{2}{{{a} - 16}}} - d},$

if 5·2²<|α|<7·2², the output value is determined as${{\frac{d}{2}{{{\alpha } - 24}}} - d},$and the output value is determined as${\frac{d}{2}{{{a} - 32}}} - d$for the other cases.

When αβ<0,

this calculation expression is obtained by substituting α with β in theexpression used for the method for determining the output of the seventhconditional probability vector explained just above (αβ≧0).

A method for obtaining the eighth to tenth conditional probabilityvectors is obtained by substituting α with β and β with α in theexpression to obtain the fifth to seventh conditional probabilityvectors.

Next, the second one of the method for demodulating square QAM signalwill be explained.

First, a soft decision method of the square QAM corresponding to thefirst form will be explained. In the case of the first form, whileanyone of the real number part and the imaginary number part among thereceived signal is used in order to calculate the conditionalprobability vector corresponding to the first half bit combination, thefirst half is demodulated using a value β and the second half isdemodulated using a value of α and it output scope is determined between1 and −1 for convenience's sake in the following description.

The method for calculating the conditional probability vectorcorresponding to the first bit in the first form can be expressed as themathematical expression β and FIGS. 3 and 11 are the visualization ofit.If |β|≧2^(n)−1, the output is determined as sign (β).   [mathematicalexpression 13]

Also, {circle around (2)}, the output is determined as 0.9375*sign(β).

Also, {circle around (3)} if 1<|β|≦2^(n)−1, the output is determined as${{{sign}(\beta)}\frac{0.0625}{2^{n} - 2}\left( {{\beta } - 1} \right)} + {0.9375*{{{sign}(\beta)}.}}$

However, the sign(β) means a sign of the value sign β.

In the first form, a method for calculating the conditional probabilityvector corresponding to the second bit can be expressed as themathematical 14 and FIGS. 4 and 12 are a visualization of it.{circle around (1)} If 2^(n)−2^(n(2−m))≦|β|≦2^(n)−2^(n(2−m))+1, theoutput is determined as (−1)^(m+1).   [mathematical expression 14]

Also, {circle around (2)} if 2^(n−1)−1≦|β|≦2^(n−1)+1, the output isdetermined as 0.9375(2^(n−1)−|β|).

Also, {circle around (3)} if2^(n−1)−2^((n−1)(2−m))+m≦|β|≦2^(n)−2^((n−1)(2−m))+m−2, the output isdetermined as${{- \frac{0.0625}{2^{n} - 2}}\left( {{\beta } - {2m} + 1} \right)} + {0.0375\left( {- 1} \right)^{m + 1}} + {0.0625.}$

Here, m=1 or m=2.

In the first form, a method for calculating the conditional probabilityvector corresponding to the third to (n−1)^(th) bits can be expressed asthe mathematical expression 15.{circle around (1)} if m*2^(n−k+2)−1≦|β|≦m*2^(n−k+2)+1, the output isdetermined as (−1)^(m+1).   [mathematical expression 15]

Also, {circle around (2)} if (2l−1)*2^(n−k+1) −1<|β|≦(2l−1)*2^(n−k+1)+1, the output is determined as (−1)^(l+1)0.9375{|β|−(2l−1)*2^(n−l+1)}.

Also, {circle around (3)} of (P−1)*2^(n−k+1) +1<|β|≦P*2^(n−k+1)−1, theoutput depends on the value P, where if the P is odd number, the outputis determined as${\frac{0.0625}{2^{n - K + 1} - 2}\left\lbrack {{\left( {- 1} \right)^{{({{({p + 1})}/2})} + 1}*{\beta }} + {\left( {- 1} \right)^{{({p + 1})}/2}\left\lbrack {{\left( {P - 1} \right)*2^{n - k + 1}} + 1} \right\rbrack} + \left( {- 1} \right)^{{({p + 1})}/2}} \right\rbrack}.$

However, if the value P is even number, the output is determined as${\frac{0.0625}{2^{n - K + 1} - 2}\left\lbrack {{\left( {- 1} \right)^{{p/2} + 1}*{\beta }} + {\left( {- 1} \right)^{p/2}\left( {{P*2^{n - k + 1}} - 1} \right)}} \right\rbrack} + {\left( {- 1} \right)^{{p/2} + 1}.}$

Here, m=0, 1 . . . 2_(k−2), and l=1, 2, . . . 2^(k−2), also, P=1, 2, . .. 2^(k−1).

Here, k is bit number, which is an integer more than 3.

In the first form, a method for calculating the conditional probabilityvector corresponding to the nth bit of the last bit in the first halfcan be expressed as the mathematical expression 16. That is a specificcase of the mathematical expression 16, wherein k=n and the onlycondition expressions of {circle around (1)} and {circle around (2)} areapplied.{circle around (1)} If m*2²−1≦|β|≦m*2²+1, the output is determined as(−1)^(m+1).

Also, {circle around (2)} if (2l−1)*2¹−1<|β|<(2l−1)*2¹+1, the output isdetermined as 0.9375{|β|−(2l−1)*2¹}.

Here, m=0, 1, . . . 2^(n−2), and l=1, 2 . . . 2^(n−2).

A method for calculating the conditional probability vectorcorresponding to the second half bits of the first form, that is, bitnumber n+1 to 2n can be performed by substituting α with β in the methodfor obtaining the conditional probability vector of the first halfaccording to the property of the first form. That is, the conditionwhere all of β in the mathematical expression is substituted with αbecomes the first conditional probability vector of the second half,that is, the conditional probability vector calculation expressioncorresponding to the (n+1)^(th) bit. Also, the conditional probabilityvector corresponding to the (n+2)^(th) bit, that is, the secondconditional probability vector of the second half can be determined bysubstituting β with α in the mathematical expression 14 that is thecondition where the second conditional probability vector of the firsthalf is calculated, and the conditional probability vector correspondingto the bit number n+3 to 2n, that is, the following cases, can bedetermined by transforming the mathematical expressions 15 and 16 asdescribed above.

Next, a soft decision method of the received signal of a square QAMcorresponding to the second form will be explained. Also, forconvenience of understanding, the value α is used to determine theconditional probability vector corresponding to the odd-ordered bit andthe value β is used to determine the even-ordered bit.

In the second form, the method for calculating the conditionalprobability vector corresponding the first bit can be expressed as themathematical expression 17 and FIG. 13 is a visualization of it.{circle around (a)} if |α|≧2^(n)−1, the output is determined as−sign(β).

Also, {circle around (b)} if |α|≦1, the output is determined as0.9375*sign(α).

Also, {circle around (c)} if 1<|α|≦2^(n)−1, the output is determined as${{- {sign}}\quad(\alpha)\frac{0.0625}{2^{n} - 2}\left( {{\alpha } - 1} \right)} + {0.9375.}$However, sign(α) means the sign of the value α.

In the second form, a method for calculating the conditional probabilityvector corresponding to the second bit can be obtained by substitutingall of α with β in the mathematical expression 17 used to calculate thefirst conditional probability vector according to the property of thesecond form.

In the second form, the method for calculating the conditionalprobability vector corresponding to the third bit can be expressed asthe mathematical expression 18.When α×β≧0   [mathematical expression 18]

{circle around (a)} if 2^(n)−2^(n(2−m))≦|α|≦2^(n)−2^(n(2−m))+1, theoutput is determined as (−1)^(m).

Also, {circle around (b)} if 2^(n−1)−1≦|α|≦2^(n−1)+1, the output isdetermined as 0.9375(|β|−2^(n−1)).

Also, {circle around (c)} if 2^(n−1)−2^((n−1))(2−m)+m≦|α|≦2^(n)−2^((n−1)(2−m))+m−2, the output is determined as${\frac{0.0625}{2^{n} - 2}\left( {{\alpha } - {2m} + 1} \right)} + {0.9735\quad\left( {- 1} \right)^{m}} - {0.0625.}$

If α×β<0, the calculation expression is determined as an expressionwhere all of α are substituted with β in the calculation expression ofthe case of α×β≧0.

As such, the method for obtaining the conditional probability vector ineach cases of α×β≧0 and α×β<0 can be said to be another property. Suchproperty is always applied when obtaining the conditional probabilityvector corresponding to the third or later bit of the second form, andthe mutual substitution property such as substituting β with α is alsoincluded in this property.

The expression for obtaining the conditional probability vectorcorresponding to the fourth bit of the second form is obtained bysubstituting α with β and β with α in the mathematical expression 18used to obtain the third conditional probability vector by the propertyof the second form in the case that the magnitude of the QAM is lessthan 64-QAM. However, the case where the magnitude of QAM is more than256-QAM is expressed as the mathematical expression 19.{circle around (a)} if m*2^(n−k+3)−1≦|α|≦m*2^(n−k+3)+1, the output isdetermined as (−1)   [mathematical expression 19]

Also, {circle around (b)} if (2l−1)*2^(n−k+2)−1<|α|≦(2l−1)*2^(n−k+2)+1,

the output is determined as(−1)^(l+1){0.9375|α|−0.9375(2l−1)*2^(n−k+2)}.

Also {circle around (c)} if (P−1)*2^(n−k+2)+1<|α|≦P*2^(n−k+2)−1,the output is determined according to the value P, where if P is an oddnumber, the output is determined as${{\frac{0.0625}{2^{n - K + 2} - 2}\left\lbrack {{\left( {- 1} \right)^{{{({p + 1})}/2} + 1}*{\alpha }} + {\left( {- 1} \right)^{{({p + 1})}/2}\left\lbrack {{\left( {P - 1} \right)*2^{n - k + 2}} + 1} \right\rbrack}} \right\rbrack} + \left( {- 1} \right)^{{({p + 1})}/2}},$

if P is an even number, the output is determined as$\left. {{\frac{0.0625}{2^{n - K + 2} - 2}\left\lbrack {{\left( {- 1} \right)^{{p/2} + 1}*{\alpha }} + {\left( {- 1} \right)^{p/2}\left( {{P*2^{n - k + 2}} - 1} \right)}} \right\rbrack} + \left( {- 1} \right)^{{p/2} + 1}} \right\rbrack.$

Here, k is a bit number, and m=0, 1, . . . 2^(k−)3, l=1, 2, . . . ,2^(k−)3, p=1, 2, . . . 2^(k−2).

An expression for obtaining the conditional probability vectorcorresponding to the fifth bit of the second form can be expressed asthe mathematical expression 20 in the case that the magnitude of QAM is64-QAM and can be applied the mathematical expression 19 in the casethat the magnitude of QAM is more than 256-QAM.When α×β≧0,   [mathematical expression 20]

{circle around (a)} if m*2²−1<|β|≦m*2²+1, the output is determined as(−1)^(m+1).

{circle around (b)} (If (2l−1)*2²−1<|β|≦(2l −1)*2²+1,

the output is determined as 0.9375(−1)^(l+1){|β|−(2l−1)*2²}.

Here, m=0, 1, 2 and l=1, 2.

If α×β<0, the output is obtained by substituting β with α in theexpressions {circle around (a)} and {circle around (b)} according to theproperty of the second form.

The calculation of the conditional probability vector corresponding tothe sixth bit of the second form is obtained by substituting α with βand β with α in the mathematical expression 20 that is an expressionused to obtain the fifth conditional probability vector according to theproperty of the second form in the case that the magnitude of QAM is64-QAM. However, a case where the magnitude of QAM is more than 256-QAMis expressed as the mathematical expression 19.

A calculation of the conditional probability vector corresponding to theseventh to n^(th) bit of the second form is determined as themathematical expression 19.

A calculation of the conditional probability vector corresponding to the(n+1)th bit of the second form is expressed as the mathematicalexpression 21 and this is a specific case of the mathematical expression19.{circle around (a)} if m*2²−1≦|α|m*2²+1, the output is determined as(−1)^(m+1).   [mathematical expression 21]

Also, {circle around (b)} If (2l−1)*2¹−1<|α|≦(2l−1)*2¹+1,

the output is determined as (−1)^(l+1){0.93751 |α|−0.9375(2l −1)*2¹}.

Here, m=0, 1, . . . 2^(n−2) and l=1, 2 . . . 2^(n−2).

A calculation of the conditional probability vector corresponding to the(n+2)^(th) bit of the second form is obtained by substituting α with βand β with α in the mathematical expression 18.

A calculation of the conditional probability vector corresponding to the(n+3)^(th) to (2n−1)^(th) bit of the second form is obtained bysubstituting α with β in the mathematical expression 19. However, thebit number of the value k that is used at this time is 4 to n, which issequentially substituted instead of n+3 to 2n−1.

A soft decision demodulation of the square QAM can be implemented usingthe received signal, that is, the value of a α+β i through such process.However, although the method described above arbitrarily decided theorder in selecting the received signal and substituting that into thedetermination expression for the convenience of understanding, it isnoted that it is applied in more general in its real application so thatthe character α or β expressed in the expression can be freely exchangedaccording to the combination constellation form of the QAM and the scopeof the output value can be asymmetrical such as a value between “a” and“b” as well as a value of “a” or “−a”. That enlarges the generality ofthe present invention and increases its significance. Also, although themathematical expressions described above seems to be very complicated,they are generalized for general applications so that it is realizedthat they are very simple viewing them through really appliedembodiments.

Third Embodiment

The third embodiment of the present invention is a case corresponding tothe first form and is applied the property of the first form. The thirdembodiment includes an example of 1024-QAM where the magnitude of QAM is1024. The order selection of the received signal is intended to apply αin the first half and β in the second half. (referring to FIGS. 11 and12).

Basically, QAM in two embodiments of the present invention can bedetermined as following expression. A mathematical expression 1determines the magnitude of QAM and a mathematical expression 2 showsthe number of bits set in each point of a combination constellationdiagram according to the magnitude of QAM.2^(2n)−QAM, n=2, 3, 4   [mathematical expression 1]then number of bits set in each point =2n   [mathematical expression 2]

Basically, the magnitude of QAM in the third embodiment of the presentinvention is determined as the following expression, and accordingly thenumber of the conditional probability vector value of the final outputvalue becomes 2n.

A case where 2^(2*5)-QAM equals to 1024-QAM according to themathematical expression 1 and the number of bits set in eachconstellation point equals to 2×5=10 bits according to the mathematicalexpression 2 will be explained when n is 5 using such mathematicalexpressions 1 and 2. First, prior to entering into calculationexpression applications, it is noted that if a calculation expressionfor 5 bits of the first half among 10 bits are known by the property ofthe first form, a calculation expression for remaining5 bits of thesecond half is also known directly.

First, for the first conditional probability vector calculationexpression,if |β|>2⁵−1, the output is determined as sign(β).

However, {circle around (2)} if |β|≦1, the output is determined as0.9375*sign(β).

Also, {circle around (3)} if 1<|β|≦2⁵−1, the output is determined as${sign}\quad{{(\beta)\left\lbrack {{\frac{0.0625}{2^{5} - 2}\left( {{\beta } - 1} \right)} + 0.9375} \right\rbrack}.}$

Next, for the second (that is, k=2, m=1, 2) conditional probabilityvector,if 0<|β|≦1, the output is determined as 1.

Also, if 2⁵−1≦|β|≦2⁵, the output is determined as −1.

Also, if 2⁴1 ≦|β|≦2⁴+1, the output is determined as 0.9375(2⁴−|β|).

Also, if 1≦|β|≦2⁴−1, the output is determined as${{{- \frac{0.0625}{2^{4} - 2}}\left( {{\beta } - 1} \right)} + 1},$andif 2⁴+1≦|β|≦2⁵−1, the output is determined as −0.0625/2⁴−2(|β|−3)−0.0825

Next, for the third (that is, k=3, m=0, 1, 2, l=1, 2, p=1, 2, 3, 4)conditional probability vector calculation expression,{circle around (1)} If m*2⁴−1≦|β|≦m*2⁴+1, the output is determined as(−1)^(m+1).

At this time, when substituting m=0, 1, 2,

if −1<|β|≦1, the output is determined as 1.

Also, if 2⁴−1<|β|≦2⁴+1, the output is determined as 1.

Also, if 2⁵−1<|β|≦2⁵+1, the output is determined as −1.

Also, {circle around (2)} if (2l−1)*2³−1<|β|≦(2l−1)*2³+1, the output isdetermined by substituting l=1,2 into (−1)^(l+1)0.9375 {|β|−(2l−1)*2³}.Here, if 2³+1, the output is determined as 0.9375(|β|−2³), and if3*2³−1<|β|≦3*2³+1, the output is determined as −0.9375(|β|−3*2³).

Also, {circle around (3)} when (P−1)*2³+1<|β|≦P*2³−1 and substitutingP=1, 2, 3 and 4 according to whether P is odd number or even number,

if 1<|β|≦2³−1, the output is determined as${{\frac{0.0625}{2^{3} - 2}\left( {{\beta } - 1} \right)} - 1},$

also, if 2³+1<|β|≦2⁴−1, the output is determined as${{\frac{0.0625}{2^{3} - 2}\left( {{\beta } - 2^{4} + 1} \right)} + 1},$

also, if 2⁴+1<|β|≦3*2³−1, the output is determined as${{\frac{0.0625}{2^{3} - 2}\left( {2^{4} + 1 - {\beta }} \right)} + 1},$

also, 3*2³+1<|β|≦2⁵−1, the output is determined as${\frac{0.0625}{2^{3} - 2}\left( {2^{5} + 1 - {\beta }} \right)} - 1.$

Next, for the fourth (that is k=4, m=0, 1, 2, 3 and 4, l=1, 2, 3 and 4,p=1, 2, 3, 4, 5, 6, 7 and 8) conditional probability vector calculationexpression,if −1<|β|≦1, the output is determined as −1.

Also, if 2³−1<|β|≦2³+1, the output is determined as 1.

Also, if 2⁴−1<|β|≦2⁴+1, the output is determined as −1.

Also, if 3*2³−1<|β|≦3*2³+1, the output is determined as 1.

Also, if 2⁵−1<|β|≦2⁵+1, the output is determined as −1.

Also, if 2²−1<|β|≦2²+1, the output is determined as 0.9375{|β|−2²}.

Also, if 3*2²−1<|β|≦3*2²+1, the output is determined as−0.9375{|β|−3*2²}.

Also, if 5*2²−1<|β|≦5*2²+1, the output is determined as0.9375{|β|−5*2²}.

Also, if 7*2²−1<|β|≦7*2²+1, the output is determined as0.9375{|β|−7*2²}. Also, if 1<|β|≦2²−1, the output is determined as${\frac{0.0625}{2^{2} - 2}\left( {{\beta } - 1} \right)} - 1.$

Also, if 2²+1<|β|≦2³1, the output is determined as${\frac{0.0625}{2^{2} - 2}\left( {{\beta } - 2^{3} + 1} \right)} + 1.$

Also, if 2³+1<|β|≦3*2²−1, the output is determined as${\frac{0.0625}{2^{2} - 2}\left( {2^{3} + 1 - {\beta }} \right)} + 1.$

Also, if 6*2²+1<|β|≦7*21²−1, the output is determined as${\frac{0.0625}{2^{2} - 2}\left( {{6*2^{2}} + 1 - {\beta }} \right)} + 1.$

Also, if 7*2²+1<|β|≦2⁵−1, the output is determined as${\frac{0.0625}{2^{2} - 2}\left( {2^{5} - 1 - {\beta }} \right)} - 1.$

Next, for the fifth (that is, k=5, m=0, 1, 2, . . . 7, 8, l=1, 2, 3, . .. 7, 8) conditional probability vector calculation expression,if −1<|β|≦1, the output is determined as −1.

Also, if 2²−1<|β|≦2²+1, the output is determined as 1.

Also, if 3*2²−1<|β|≦3*2²+1, the output is determined as −1.

Also, if 7*2²−1<|β|≦7*2²+1, the output is determined as 1.

Also, if 2⁵−1<|β|≦2⁵+1, the output is determined as −1.

Also, if 1<|β|≦3, the output is determined as 0.9375(|β|−2).

Also, if 5<|β|≦7, the output is determined as −0.9375(|β|−6).

Also, if 9<|β|≦11, the output is determined as 0.9375(|β|−10).

Also, if 25<|β|≦27, the output is determined as 0.9375(|β|−26).

Also, if 29<|β|≦31, the output is determined as −0.9375(|β|−30).

Next, the calculation expressions of the sixth to tenth conditionalprobability vectors can be obtained by substituting β with α in thefirst to fifth conditional probability vector according to the propertyof the first form.

Fourth Embodiment

The fourth embodiment of the present invention is a case correspondingto the second form and is applied the property of the second form. Thefourth embodiment includes an example of 1024-QAM where the magnitude ofQAM is 1024. The order selection of the received signal is intended toapply α at first.

A mathematical expression 1 determines the magnitude of QAM and amathematical expression 2 shows the number of bits set in each point ofa combination constellation diagram according to the magnitude of QAM,as is in the third embodiment.2^(2n)-QAM, n=2, 3, 4   [mathematical expression1]the number of bits set in each point=2n   [mathematical expression 2]

Basically, the magnitude of QAM in the fourth embodiment of the presentinvention is determined as the above expression, and accordingly thenumber of the conditional probability vector value of the final outputvalue becomes 2n.

A case where 2^(2*5)-QAM equals to 1024-QAM according to themathematical expression 1 and the number of bits set in eachconstellation point equals to 2×5=10 bits according to the mathematicalexpression 2 will be explained when n is 5 using such mathematicalexpressions 1 and 2. (referring to FIGS. 13 and 14).

First, for the calculation of the first conditional probability vector,if |α|>2⁵−1, the output is determined as −sign(α).

Also, if |α|≦1, the output is determined as −0.9375sign(α).

Also, if 1<|α|≦2⁵−1, the output is determined as$- {{{{sign}(\alpha)}\left\lbrack {{\frac{0.0625}{2^{5} - 2}\left( {{\alpha } - 1} \right)} + 0.9375} \right\rbrack}.}$

Next, the second conditional probability vector calculation expressionis a substitution form of the first calculation expression as follows.{circle around (a)} If |β|>2⁵−1, output is determined as −sign(β).{circle around (b)} if |β|≦1, the output is determined as −0.9375sign(β).{circle around (c)} if 1<|β|≦2⁵−1, the output is determined as−sign(β){0.0021(|β|−1)+0.9375.

Next, for the third conditional probability vector calculationexpression, when αβ≧0,{circle around (a)} if 2⁵−2^(5(2−m))≦|α|<2⁵−2^(5(2−m))+1, the output isdetermined as (−1)^(m).

At this time, since m equals to 1 and 2, when substituting that, if0≦|α|<1, the output is determined as −1.

Also, if 2⁵−1≦|α|<2⁵, the output is determined as 1.

Also, {circle around (e)} if 2⁴−1≦|α|<2⁴+1, the output is determined as0.9375(|α|−2⁴).

Also, {circle around (c)} if 2⁴−2^(4(2−m))m≦|α|<2⁵−2^(4(2−m))+m−2, theoutput is determined as${\frac{0.0625}{2^{4} - 2}\left( {{\alpha } - {2m} + 1} \right)} + {0.9735\left( {- 1} \right)^{m}} - {0.0625.}$

Here, when substituting m=1, 2,

if 1≦|α|<2⁴−1, the output is determined as${\frac{0.0625}{2^{4} - 2}\left( {{\alpha } - 1} \right)} - 1.$

Also, if 2⁴+1≦|α|<2⁵−1, the output is determined as${\frac{0.0625}{2^{4} - 2}\left( {{\alpha } - 3} \right)} + {0.825.}$

When αβ<0, in this case, the calculation expression is obtained bysubstituting α with β in the expressions {circle around (a)}, {circlearound (b)}, {circle around (c)} of the method for determining theoutput of the third conditional probability vector described just above.

Next, for the fourth (that is, k=4, m=0, 1, 2, l=1, 2, p=1, 2, 3, 4)conditional probability vector calculation,

When αβ≧0,{circle around (a)} if m*2⁴−1≦|α|<m*2⁴+1, the output is determined as(−1)^(m+1).

At this time, substituting m=0, 1, 2, if −1<|α|≦1, the output isdetermined as −1.

Also, if 2⁴−1≦|α|<2⁴+1, the output is determined as 1.

Also, if 2⁵−1≦|α|<2⁵+1, the output is determined as 1.

Also, {circle around (b)} of (2l−1)*2³ −1≦|α|<(2l−1)*b 2 ³+1, the outputis determined by substituting l=1, 2 in the(−1)^(l+t){0.9375|α|−0.9375(2l−1)*2³},

here, if 2³−1≦|α|<2³+1, the output is determined as 0.9375(|α|−2³).

Also, if 3*2³−1≦|α|≦(3*2³+1, the output is determined as−0.9375(|α|−3*2³).

Also, {circle around (c)} if (P−1)*2³−1 and P is an odd number, theoutput is determined as${\frac{0.0625}{2^{3} - 2}\left\lbrack {{\left( {- 1} \right)^{{{({p + 1})}/2} + 1}*{\alpha }} + {\left( {- 1} \right)^{{({p + 1})}/2}\left( {P - 1} \right)*2^{3}} + 1} \right\rbrack} + {\left( {- 1} \right)^{{({p + 1})}/2}.}$

However, if P is an even number,

the output is determined as${\frac{0.0625}{2^{3} - 2}\left\lbrack {{\left( {- 1} \right)^{{p/2} + 1}*{\alpha }} + {\left( {- 1} \right)^{p/2}\left( {{P*2^{3}} - 1} \right)}} \right\rbrack} + {\left( {- 1} \right)^{{p/2} + 1}.}$

Here, when substituting p=1, 2, 3, 4,

if 1<|α|≦2³−1, the output is determined as${\frac{0.0625}{2^{3} - 2}\left\lbrack {{\alpha } - 1} \right\rbrack} - 1.$

Also, if 2³+1<|α|≦2⁴−1, the output is determined as${\frac{0.0625}{2^{3} - 2}\left\lbrack {{\alpha } - 2^{4} + 1} \right\rbrack} + 1.$

Also, if 2⁴+1<|α|≦3*2³−1, the output is determined as${\frac{0.0625}{2^{3} - 2}\left\lbrack {2^{4} + 1 - {\alpha }} \right\rbrack} + 1.$

Also, if 3*2³+1<|α|≦2⁵−1, the output is determined as${\frac{0.0625}{2^{3} - 2}\left\lbrack {2^{5} + 1 - {\alpha }} \right\rbrack} - 1.$

When αβ<0,

in this case, the calculation expression is obtained by substituting αwith β in the expressions of {circle around (a)}, {circle around (b)},{circle around (c)} of the method for determining the output of thefourth conditional probability vector described just above.

Next, for the fifth (that is, k=5, m=0, 1, 2, 3, 4, l=1, 2, 3, 4)conditional probability vector,

(1) when αβ≧0,{circle around (a)} if m*2³−1<|α|≦m*2³+1, the output is determined as(−1)^(m+1).

At this time, when substituting m=0, 1, 2, 3, 4,

if −1<|α|≦, the output is determined as −1.

Also, if 2³−1<|α|≦2³+1, the output is determined as 1.

Also, if 2⁴−1<|α|≦2⁴+1, the output is determined as −1.

Also, if 3*2³−1<|α|≦3*2³+1, the output is determined as 1.

Also, if 2⁵−1<|α|≦2⁵+1, the output is determined as −1.

Also, {circle around (b)} if (2l−1)*2²−1<|α|≦(2l−1)*2²+1, the output isdetermined by substituting l=1, 2, 3, 4 in the

(−1)^(l+1)0.9375{|α|−0.9375(2l−1)*2²},

here, if 2²−1<|α|≦2²+1, the output is determined as 0.9375(|α|−2²).

Also, if 3*2³−1<|α|≦3*2³+1, the output is determined as−0.9375(|α|−3*2²).

Also, if 5*2²−1<|α|≦5*2²+1, the output is determined as0.9375(|α|−5*2²).

Also, if 7*2²−1<|α|≦7*2²+1, the output is determined as−0.9375(|α|−7*2²).

Also, {circle around (c)} when (P−1)*2² +1<|α|≦P*2²−1, and substitutingp=1, 2, 3, . . . 7, 8 according to whether P is an odd number or an evennumber,

if 1<|α|≦2²−1, the output is determined as${\frac{0.0625}{2^{2} - 2}\left\lbrack {{\alpha } - 1} \right\rbrack} - 1.$

Also, if 2²+1<|α|≦2³−1, the output is determined as${\frac{0.0625}{2^{2} - 2}\left\lbrack {{\alpha } - 2^{3} + 1} \right\rbrack} + 1.$

Also, if 2³+1<|α|≦3*2²−1, the output is determined as${\frac{0.0625}{2^{2} - 2}\left\lbrack {2^{3} + 1 - {\alpha }} \right\rbrack} + 1.$

Also, if 3*2²+1<|α|≦2⁴−1, the output is determined as${\frac{0.0625}{2^{2} - 2}\left\lbrack {2^{4} - 1 - {\alpha }} \right\rbrack} - 1.$

Also, if 2⁴+1<|α|≦5*2²−1, the output is determined as${\frac{0.0625}{2^{2} - 2}\left\lbrack {{\alpha } - 2^{4} - 1} \right\rbrack} - 1.$

Also, if 5*2²+1<|α|≦6*2²−1, the output is determined as${\frac{0.0625}{2^{2} - 2}\left\lbrack {{\alpha } - {6*2^{2}} + 1} \right\rbrack} + 1.$

Also, if 6*2²+1<|α|≦7*2²−1, the output is determined as${\frac{0.0625}{2^{2} - 2}\left\lbrack {{6*2^{2}} + 1 - {\alpha }} \right\rbrack} + 1.$

Also, if 7*2²+1<|α|≦2⁵−1, the output is determined as${\frac{0.0625}{2^{2} - 2}\left\lbrack {2^{5} - 1 - {\alpha }} \right\rbrack} - 1.$

When αβ<0,

in this case, the calculation expression is obtained by substituting αwith β in the {circle around (a)}, {circle around (b)}, {circle around(c)} expressions of the method for determining the fifth conditionalprobability vector (αβ<0) described just above.

Next, for the sixth conditional probability vector (that is, k=6, m=0,1, 2, . . . 7, 8, l=1, 2, 3, . . . 7, 8),

(1) when αβ≧0,{circle around (a)} if m*2²−1<|α|≦m*2²+1, the output is determined as(−1)^(m+1).

At this time, the output is obtained by applying m=0, 1, 2, . . . 7, 8.

That is, if −1<|α|≦1, the output is determined as −1.

Also, if 2²−1<|α|≦2²+1, the output is determined as 1.

Also, if 3*2²−1<|α|3*2²+1, the output is determined as −1.

Also, if 7*2²−1<|α|≦7*2²+1, the output is determined as 1.

Also, if 2⁵−1<|α|≦2^(5+1,) the output is determined as −1.

Also, {circle around (b)} if (2l−1)*2−1<|α|≦(2l−1)*2+1, the output isdetermined by substituting l=1, 2, 3, . . . 7,8 in the(−1)^(l+1){0.9375|α|−0.9375(2l −1)*2},

here, if 1<|α|≦7, the output is determined as 0.9375(|α|−−2).

Also, if 5<|α|≦7, the output is determined as −0.9375(|α|−6).

Also, if 9<|α|≦11, the output is determined as 0.9375(|α|−10).

Also, if 25<|α|≦27, the output is determined as 0.9375(|α|−26).

Also, if 29<|α|≦31, the output is determined as −0.9375(|α|−30).

2 When αβ<0,

in this case, the calculation expression is obtained by substituting αwith β in the

{circle around (a+EE, {circle around (b)} expressions of the method fordetermining the output of the fifth conditional probability vector(αβ≦0) described just above.

Next, the calculation expressions of the seventh to tenth conditionalprobability vector are obtained by substituting α with β and β with a inthe calculation expressions of the third to sixth conditionalprobability vector.

FIG. 11 is a view showing a functional block for a conditionalprobability vector decision process in accordance with the presentinvention.

FIG. 12 is a view showing an example of hard ware configuration for aconditional probability vector of a first form of 64-QAM in accordancewith the present invention. A person skilled in the art can configurethe hard ware by making a modification within the scope of the presentinvention.

While the present invention has been described in conjunction withpreferred embodiments thereof, it is not limited by the foregoingdescription, but embraces alterations, modifications and variations inaccordance with the spirit and scope of the appended claims.

INDUSTRIAL APPLICABILITY

In accordance with the present invention, it is expected to enhance theprocess speed remarkably and to save a manufacturing cost upon embodyinghard ware by applying a linear conditional probability vector equationinstead of a log likelihood ratio method being soft decisiondemodulation method of a square QAM signal that is generally used in theindustrial field.

1. A soft decision method for demodulating a received signal of a squareQuadrature Amplitude Modulation (QAM) consisted of an in-phase signalcomponent and a quadrature phase signal component, wherein a conditionalprobability vector value being each soft decision value corresponding toa bit position of a hard decision is obtained using a function includinga conditional determination operation from the quadrature phasecomponent and the in-phase component of the received signal.
 2. Themethod according to claim 1, wherein the conditional probability vectordecision method for a first half of total bits is the same as thedecision method for the remaining half of bits, which is determined bysubstituting the quadrature phase component value and the in-phasecomponent value each other.
 3. The method according to claim 2, whereinthe conditional probability vector values corresponding to a first ton^(th) bit are demodulated by one of the received signal α and β, andthe conditional probability vector values corresponding to the(n+1)^(th) to 2n^(th) bits of the second half are demodulated by theremaining received signal, and equation applied for the twodemodulations has the same method in the first half and the second half.4. The method according to claim 2, wherein the demodulation method ofthe conditional probability vector corresponding to an odd-ordered bitis the same as a calculation method of the conditional probabilityvector corresponding to the next even-ordered bit, where the receivedsignal value used to calculate the conditional probability vectorcorresponding to the odd-ordered bit uses one of the α and β accordingto a given combination constellation diagram and the received signalvalue for the even-ordered bit uses the remaining one.
 5. The methodaccording to claim 3, wherein the first conditional probability vectoris determined by selecting one of the received values α with β accordingto the combination constellation diagram and applying a followingmathematical expression 22, where in the mathematical expression 22,{circle around (1)} an output value is unconditionally determined as$\frac{a}{2^{n}}\Omega$ [here, Ω is a selected and received value whichis one of α and β, and α is an arbitrary real number set according to adesired output scope].
 6. The method according to claim 3, wherein thesecond conditional probability vector is determined by the receivedvalue selected when determining the first conditional probability vectorand a following mathematical expression 23, where, in the mathematicalexpression 23, {circle around (1)} the output value is unconditionallydetermined as $a\left( {c - {\frac{c}{2^{n - 1}}{\Omega }}} \right)$[here, Ω is a selected and received value, n is a magnitude of the QAM,that is, a parameter used to determine 2^(2n), a is an arbitrary realnumber set according to a desired output scope, and c is an arbitraryconstant].
 7. The method according to claim 3, wherein the third ton^(th) conditional probability vectors are determined by a receivedvalue set when determining the first conditional probability vector anda following mathematical 24, where in the mathematical expression 24,first, dividing an output diagram in a shape of a basic V form, theconditional probability vector corresponding to each bit is divided into(2^(k−3)+1) areas, the basic expression according to the basic form isdetermined as$a\left( {{\frac{d}{2^{n - k + 1}}{\Omega }} - d} \right)$ {circlearound (3)} the output is determined by finding an involved area usingthe given Ω and substituting a value of (|Ω|−m) that a middle value issubtracted from each area into the basic expression as a new Ω, {circlearound (4)} rendering the middle value as m=2^(n) and substituting thevalue of (|Ω|−m) into the basic expression as a new Ω in an area that isin the most outer left and right sides among the divided areas, that is,(2^(k−2)−1)2^(n−k+2)<|Ω|, [here, Ω is a selected and received value, nis a magnitude of the QAM, that is, a parameter used to determine2^(2n), k is conditional probability vector number (k=3, 4, . . . , n),d is a constant that changes according to the value of k, and a is aconstant determining the output scope].
 8. The method according to claim3, wherein the (n+1)^(th) to 2n^(th) conditional probability vectors aresequentially obtained using the received value that is not selected whenthe first conditional probability vector is determined and themathematical expressions described above (however, the number k of theconditional probability vector included in the mathematical expression24 sequentially substitutes 3 to n with n+1 to 2n).
 9. The methodaccording to claim 4, the first conditional probability vector isdetermined by selecting any one of the received values α and β accordingto a form of the combination constellation diagram and then according toa mathematical expression 25, where in the mathematical expression 25,{circle around (a)} the output value is unconditionally determined as${- \frac{a}{2^{n}}}\Omega$ [here, Ω is a selected and received valuethat is one of α and β, n is a magnitude of the QAM, that is, aparameter used to determine 2^(2n), and a is an arbitrary real numberset according to a desired output scope].
 10. The method according toclaim 4, wherein the second conditional probability vector performs acalculation by substituting the received value selected with thereceived value that is not selected in the method for obtaining thefirst conditional probability vector of the second form.
 11. The methodaccording to claim 4, wherein the third conditional probability vectorselects one of the received values α and β according to a form of thecombination constellation diagram, uses a following mathematicalexpression 26 in the case of αβ≧0, and determines by substituting thereceived value selected in the mathematical expression 26 with thereceived value that is not selected in the expression in the case ofαβ<0, where in the mathematical expression 26, the output value isdetermined as $a\left( {c - {\frac{c}{2^{n - 1}}{\Omega }}} \right)$[here, Ω is a selected and received value, n is a magnitude of the QAM,that is, a parameter used to determine 2^(2n), a is an arbitrary realnumber set according to a desired output scope, and c is an arbitraryconstant].
 12. The method according to claim 4, wherein the fourthconditional probability vector is calculated by substituting each ofreceived values used with each of the received values that are not usedin the method for obtaining the third conditional probability vector ofthe second form in the cases of αβ≧0 and αβ<0.
 13. The method accordingto claim 4, wherein the fifth conditional probability vector selects oneof the received values α and β according to the form of the combinationconstellation diagram, uses a following mathematical expression 27 inthe case of αβ≧0, and determines by substituting the received valueselected in the mathematical expression 27 with the received value thatis not selected in the expression in the case of αβ<0, where in themathematical expression 27, {circle around (1)} first, dividing anoutput diagram in a shape of a basic V form, the conditional probabilityvector corresponding to each bit is divided into 2 areas, {circle around(2)} the basic expression according to the basic form is determined as${a\left( {{\frac{d}{2^{{\cdot n} - 2}}{\Omega }} - d} \right)},${circle around (3)} the output is determined by finding an involved areausing the given Ω and substituting a value of (|Ω|−m) that a middlevalue is subtracted from each area into the basic expression as a new Ω.{circle around (4)} rendering the middle value as m=2^(n) andsubstituting the value of |Ω|−m into the basic expression as a new Ω inan area that is in the most outer left and right sides among the dividedareas, that is, 7·2^(n−3)<|Ω|, [here, Ω is a selected and receivedvalue, n is a magnitude of the QAM, that is, a parameter used todetermine 2^(2n), d is a constant, and a is a constant determining theoutput scope].
 14. The method according to claim 4, wherein when themagnitude of QAM is 64-QAM, the sixth conditional probability vector iscalculated by substituting each of received values used with each of thereceived values that are not used in the method for obtaining the fifthconditional probability vector of the second form in the cases of αβ≧0and αβ<0.
 15. The method according to claim 4, wherein when themagnitude of QAM is more than 256-QAM, the fifth to (n+2)^(th)conditional probability vector select one of the received values α and βaccording to the form of the combination constellation diagram, isdetermined by a following mathematical expression 28 in the case ofαβ≧0, and determines by substituting the received value selected in themathematical expression 28 with the received value that is not selectedin the expression in the case of αβ<0, where in the mathematicalexpression 28, {circle around (1)} first, dividing an output diagram ina shape of a basic V form, the conditional probability vectorcorresponding to each bit is divided into (2^(k−5)+1) areas, {circlearound (2)} the basic expression according to the basic form isdetermined as${a\left( {{\frac{d}{2^{n - k + 3}}{\Omega }} - d} \right)},$ {circlearound (3)} the output is determined by finding an involved area usingthe given Ω and substituting a value of |Ω|−m that a middle value m (forexample, in the case of k=6, since repeated area is 1, this area is2^(n−2)≦|Ω|<3·2^(n−2) and the middle value is m=2^(n−1)) is subtractedfrom each area into the basic expression as a new Ω, {circle around (4)}rendering the middle value as m=2^(n) and substituting the value of|Ω|−m into the basic expression as a new Ω in an area that is in themost outer left and right sides among the divided areas, that is,(2^(k−2)−1)2^(n−k+2)<|Ω|, [here, k is the conditional probability vectornumber (5, 6, . . .n), Ω is a selected and received value, n is amagnitude of the QAM, that is, a parameter used to determine 2^(2n), ais a constant determining the output scope, and d is a constant thatchanges according to a value of k].
 16. The method according to claim 4,wherein when the magnitude of QAM is more than 256-QAM, the (n+3)^(th)to (2n)^(th) conditional probability vectors is selected by themathematical expression 28 using the received value that is not selectedwhen determining the fifth to (n+2)^(th) conditional probability vectorof the second form in the case of αβ≧0, and is obtained by substitutingthe received value selected in the mathematical expression 28 with thereceived value that is not selected in the expression in the case ofαβ<0.
 17. The method according to claim 3, wherein the first conditionalprobability Vector of the first form is determined by selecting any oneof the received values α and β according to a form of the combinationconstellation diagram and then according to a mathematical expression29, where in the mathematical expression 29, {circle around (1)} if|Ω|≧2^(n)−1, the output is determined as *sign(Ω), also, {circle around(2)} |Ω|≦1, the output is determined as a*0.9375*sign(Ω), also, {circlearound (3)} 1<|Ω|≦2^(n)−1 the output is determined as${a*{{{sign}(\Omega)}\left\lbrack {{\frac{0.0625}{2^{n} - 2}\left( {{\Omega } - 1} \right)} + 0.9375} \right\rbrack}},$[here, Ω is anyone of the received values α and β, ‘sign(Ω)’ indicatesthe sign of the selected and received value, ‘a’ is an arbitrary realnumber set according to a desired output scope, α is a received value ofI (real number) channel, and β is a received value of Q(imaginarynumber) channel].
 18. The method according to claim 3, wherein thesecond conditional probability vector of the first form is determined bythe received value selected when determining the first conditionalprobability vector and the mathematical expression 30, where in themathematical expression 30 {circle around (1)} if2^(n)−2^(n(2−m))≦|Ω|≦2^(n)−2^(n(2−m)+1, the output is determined as a*(−1)^(m+1), {circle around (2)} if 2^(n−1)−1≦|Ω|≦2^(n−1)+1, the outputis determined as a*0.9375(2^(n−1)−|Ω|), {circle around (3)} if2^(n−1)−2^((n−1)(2−m)) +m≦|Ω|≦2^(n)−2^((n−1)(2−m)) m−2, the output isdetermined as${{- a}*\left\lbrack {{\frac{0.0625}{2^{n} - 2}\left( {{\Omega } - {2m} + 1} \right)} + {0.9735\left( {- 1} \right)^{m + 1}} + 0.0625} \right\rbrack},$here, Ω is a selected and received value, n is the magnitude of QAM,that is, a parameter used to determine 2^(2n), ‘a’ is an arbitrary realnumber set according to a desired output scope, and m=1, 2].
 19. Themethod according to claim 3, wherein the third to (n−1)^(th) conditionalprobability vectors of the first form are determined by the receivedvalue selected when determining the first conditional probability vectorand the mathematical expression 31, where in the mathematical expression30, {circle around (1)} if m*2^(n−k+2)−1<|Ω|≦m*2^(n−k+2)+1, the outputis determined as a *(−1)^(m+1,) also, {circle around (2)} if(2l−1)*2^(n−k+1) −1<|Ω|≦(2l−1)*2^(n−k+)+1, the output is determined asa*(−1)^(l+1)0.9375{(|Ω|−(2l−1)*2^(n−k+1)), also, {circle around (3)} if(P−1)*2^(n−k+1)+1<|Ω|≦P*2^((n−k+1)−1, when P is an odd number, theoutput is determined as${a*\left\lbrack {\frac{0.0625}{2^{n - k + 1} - 2}\left\lbrack \quad{{\left( {- 1} \right)^{{{({p + 1})}/2} + 1}*{\Omega }} + {\left( {- 1} \right)^{{({p + 1})}/2}\left\lbrack {{\left( {P - 1} \right)*2^{n - k + 1}} + 1} \right\rbrack} + \left( {- 1} \right)^{{({p + 1})}/2}} \right\rbrack} \right\rbrack},$when P is an even number, the output is determined as${a*\left\lbrack {{\frac{0.0625}{2^{n - k + 1} - 2}\left\lbrack \quad{{\left( {- 1} \right)^{{p/2} + 1}*{\Omega }} + {\left( {- 1} \right)^{p/2}\left( {{P*2^{n - k + 1}} - 1} \right)}} \right\rbrack} + \left( {- 1} \right)^{{p/2} + 1}} \right\rbrack},$[here, Ω is a selected and received value, m=0, 1, . . . 2^(k−2), and lis 1, 2, . . . 3^(k−2), k is conditional probability vector number (k=3,. . . n−1)].
 20. The method according to claim 3, wherein the n^(th)conditional probability Vector of the first form is determined by thereceived value selected when determining the first conditionalprobability vector and the mathematical expression 32, where in themathematical expression 32, {circle around (1)} ifm*2²−1≦|Ω|≦m*2^(n2)+1, the output is determined as a *(−1)^(m+1), also,{circle around (2)} if (2−1)*2¹ −1<|Ω|≦(2l−1)*2¹+1, the output isdetermined as a*(−1)^(l+1)0.9375{(|Ω|−(2l−1)*2¹), [here, Ω is a selectedand received value, m=0, 1, . . . 2^(n−2), and l=1, 2, . . . 3^(n−2)].21. The method according to claim 3, wherein the (n+1)^(th) to 2n^(th)conditional probability vectors of the first form are sequentiallyobtained using the received value that is not selected when determiningthe first conditional probability vector and the mathematicalexpressions 30 to 32, respectively [however, the conditional probabilityvector number k included in the mathematical expression 31 issequentially used as 3 to n−1 instead of n+3 to 2n−1].
 22. The methodaccording to claim 4, wherein the first conditional probability Vectorof the second form is determined by selecting any one of the receivedvalues α and β according to a form of the combination constellationdiagram and then according to a mathematical expression 33, where in themathematical expression 33, {circle around (1)} if |Ω|≧2^(n)−1, theoutput is determined as −a*sign(Ω), also, {circle around (2)} |Ω|≦1, theoutput is determined as a*0.9375*sign(Ω), also, {circle around (3)} 1<|Ω|≦2^(n)−1, the output is determined as${{- a}*\left\lbrack {{{{sign}(\Omega)}\frac{0.0625}{2^{n} - 2}\left( {{\Omega } - 1} \right)} + {0/9275}} \right\rbrack},$[here, Ω is the selected and received value, ‘sign(Ω)’ indicates thesign of the selected and received value, a is an arbitrary real numberset according to a desired output scope, α is a received value of I(real number) channel, and β is a received value of Q (imaginary number)channel].
 23. The method according to claim 4, wherein the secondconditional probability vector of the second form is calculated bysubstituting the received value selected in the method for obtaining thefirst conditional probability vector of the second form with thereceived value that is not selected in the method.
 24. The methodaccording to claim 4, wherein the third conditional probability vectorof the second form selects anyone of the received values α and βaccording to the combination constellation diagram, and determines usingthe following mathematical expression 34 in the case of α*β≧0, andsubstituting the selected and received value in the mathematicalexpression 34 with the received value that is not selected in themathematical expression 34 in the case of α*β<0, where in themathematical expression 34, {circle around (1)} if2^(n)−2^(n(2−m))≦|Ω|≦2^(n)−2^(n(2−m))+1, the output is determined as a*(−1)^(m), also {circle around (2)} if 2^(n−1)−1≦|Ω|≦2^(n−1)+1, theoutput is determined as a *0.9375(|Ω|−2^(n−1)), also, {circle around(3)} if 2^(n−1)−2^((n−1)(2−m))+m≦|Ω|≦2^(n)−2^((n−1)(2−m))+m−2, theoutput is determined as${a*\left\lbrack {{\frac{0.0625}{2^{n} - 2}\left( {{\Omega } - {2m} + 1} \right)} + {0.9735\left( {- 1} \right)^{m}} - 0.0625} \right\rbrack},$[here, Ω is a selected and received value, ‘a’ is an arbitrary realnumber set according to a desired output scope, α is a received value ofI (real number) channel, β is a received value of Q(imaginary number),and m=1,2].
 25. The method according to claim 4, wherein when themagnitude of QAM of the second form is less than 64-QAM, the fourthconditional probability vector is calculated by substituting each ofreceived values used with each of the received values that are not usedin the method for obtaining the third conditional probability vector ofthe second form in the cases of α*β≧0 and α*β<0.
 26. The methodaccording to claim 4, wherein when the magnitude of QAM of the secondform is 64-QAM, the fifth conditional probability vector select one ofthe received values α and β according to the form of the combinationconstellation diagram, and determines using the following mathematicalexpression 35 in the case of α*β≧0, and substituting the received valueselected in the mathematical expression 35 with the received value thatis not selected in the expression in the case of α*β<0, where in themathematical expression 35, {circle around (1)} ifm*2^(n−1)−1≦|Ω|≦m*2^(n−1)+1, the output is determined as a *(−1)^(m+1).also, {circle around (2)} if (2l−1)*2^(n−1) −1<|Ω|≦(2l−1)*2^(n−1)+1, theoutput is determined as a*(−1)^(l+1){0.9375 |β|−0.9375(2l−1)*2^(n−1)},[here, Ω is a selected and received value, ‘a’ is an arbitrary realnumber set according to a desired output scope, α is a received value ofI (real number) channel, β is a received value of Q (imaginary number)channel, m=0, 1, 2, and l=1, 2].
 27. The method according to claim 4,wherein when the magnitude of QAM of the second form is 64-QAM, thesixth conditional probability vector is calculated by substituting eachof received values used with each of the received values that are notused in the method for obtaining the fifth conditional probabilityvector of the second form in the cases of α*β≧0 and α*β<0.
 28. Themethod according to claim 4, wherein when the magnitude of QAM of thesecond form is more than 256-QAM, the fourth to n^(th) conditionalprobability vectors select one of the received values α and β accordingto the form of the combination constellation diagram, is determined by afollowing mathematical expression 36 in the case of α*β≧0, anddetermines by substituting the received value selected in themathematical expression 36 with the received value that is not selectedin the expression in the case of α*β<0, where in the mathematicalexpression 36, where in the mathematical expression 36, {circle around(a)} if m*2^(n−k+3) −1<|Ω|≦m*2^(n−k+3)+1, the output is determined as a*(−1)^(m+1), also, {circle around (b)} if (2l−1)*2^(n−k+2)−1<|Ω|≦(2l−1)*2^(n−k+2)+1, the output is determined asa*(−1)^(l+1){0.9375(|Ω|−0.9375(2l−1)*2^(n−k+2)), also, {circle around(c)} if (*P−1)*2^(n−k+2)+1<|Ω|≦P*2^(n−k+2)−1, when P is an odd number,the output is determined asβ*0.0625/2^(n−K+1)−2[(−1)^((p+1)/2+1)*|Ω|+(−1)^((p+1)/2)[(P−1)*2^(n−k+2)+1]]+(−1)^((p+)1)/2],when P is an even number, the output is determined as${a*\left\lbrack {{\frac{0.0625}{2^{n - k + 1} - 2}\left\lbrack \quad{{\left( {- 1} \right)^{{p/2} + 1}*{\Omega }} + {\left( {- 1} \right)^{p/2}\left( {{P*2^{n - k + 2}} - 1} \right)}} \right\rbrack} + \left( {- 1} \right)^{{p/2} + 1}} \right\rbrack},$[here, k is conditional probability vector numbers (4, 5, . . . , n), Ωis a selected and received value, ‘a’ is an arbitrary real number setaccording to a desired output scope, α is a received value of I (realnumber) channel, β is a received value of Q (imaginary number) channel,m=0, 1, . . . 2^(k−3), l is 1, 2, . . . 3^(k−3), and p=1, 2 . . . ,2^(k−2)].
 29. The method according to claim 4, wherein when themagnitude of QAM of the second form is more than 256-QAM, the (n+1)^(th)conditional probability vectors is a received value selected whendetermining the fourth to n^(th) conditional probability vector of thesecond form, is determined using the mathematical expression 37 in thecase of α*β≧0, and is obtained by substituting the received valueselected in the mathematical expression 37 with the received value thatis not selected in the expression in the case of α*β<0, where in themathematical expression 37, {circle around (a)} if m*2²−1≦|Ω|≦m*2²+1,the output is determined as a*(−1)^(m+1), also, {circle around (b)}if(2l−1)*2¹−1<|Ω|≦(2l−1)*2¹+1, the output is determined asa*(−1)^(l+1){0.9375{(|Ω|−0.9375(2t−1)*2¹), [here, Ω is a selected andreceived value, ‘a’ is an arbitrary real number set according to adesired output scope, α is a received value of I (real number) channel,β is a received value of Q (imaginary number) channel, m=0, 1, . . .2^(k−2), and l is 1, 2, . . . 3^(k−2)].
 30. The method according toclaim 4, wherein when the magnitude of QAM of the second form is morethan 256-QAM, the method for obtaining the (n+2)^(th) conditionalprobability vector is the same as the method for obtaining the fourthconditional probability vector in the case that the magnitude of QAM ofthe second form is less than 256-QAM.
 31. The method according to claim4, wherein when the magnitude of QAM of the second form is more than256-QAM, the (n+3)^(th) to (2n−1)^(th) conditional probability vectorsare calculated by substituting each of received values used with each ofthe received values that are not used when determining the fourth ton^(th) conditional probability vectors in the cases of α*β≧0 and α*β<0when the magnitude of QAM of the second form is more than 256-QAM. 32.The method according to claim 4, wherein when the magnitude of QAM ofthe second form is more than 256-QAM, the 2^(th) conditional probabilityvector is calculated by substituting each of received values used witheach of the received values that are not used when determining thefourth to the (n+1)^(th) conditional probability vector in the cases ofα*β≧0 and α*β<0 when the magnitude of QAM of the second form is morethan 256-QAM.
 33. An apparatus for demodulating an QAM receiving signalconsisted of an in-phase signal component and an quadrature phase signalcomponent, wherein the apparatus comprises a conditional probabilityvector determination unit for obtaining a conditional probability vectorvalue being each soft decision value corresponding to a bit position ofa hard decision is obtained using a function including a conditionaldetermination operation from the quadrature phase component and thein-phase component of the received signal.
 34. The apparatus accordingto claim 33, wherein in the conditional probability vector determinationunit, an operation for determining the conditional probability vectorfor a first half of total bits is the same as an operation fordetermining the conditional probability vector for the remaining halfbits, and is determined by substituting the quadrature phase componentvalue with the in-phase component value, respectively.
 35. The apparatusaccording to claim 33, wherein in the conditional probability vectoroperation unit, the conditional probability vector values correspondingto the first to n^(th) bits are demodulated by anyone of the receivedsignals α and β, and the conditional probability vector valuescorresponding to the (n+1)^(th) to the 2n^(th) bits of the second halfare demodulated by the received signal of the remaining one, and firsthalf and second half equations applied to the two demodulations aresame.
 36. The apparatus according to claim 33, wherein in theconditional probability vector operation unit, the demodulationoperation of the conditional probability vector corresponding to anodd-ordered bit is identical to the operation of the conditionalprobability vector corresponding to the next even-ordered bit, and thereceived signal value to calculate the conditional probability vectorcorresponding to the odd-ordered bit uses anyone of α and β according toa given combination constellation diagram, and the received signal valuefor the even-ordered bit uses the remaining one.
 37. The apparatusaccording to claim 34, wherein in the conditional probability vectoroperation unit, the conditional probability vector values correspondingto the first to n^(th) bits are demodulated by anyone of the receivedsignals α and β and the conditional probability vector valuescorresponding to the (n+1)^(th) to the 2n^(th) bits of the second halfare demodulated by the received signal of the remaining one, and firsthalf and second half equations applied to the two demodulations aresame.
 38. The apparatus according to claim 34, wherein in theconditional probability vector operation unit, the demodulationoperation of the conditional probability vector corresponding to anodd-ordered bit is identical to the operation of the conditionalprobability vector corresponding to the next even-ordered bit, and thereceived signal value to calculate the conditional probability vectorcorresponding to the odd-ordered bit uses anyone of α and β according toa given combination constellation diagram, and the received signal valuefor the even-ordered bit uses the remaining one.